General local properties of fuzzy relations and fuzzy multisets used to an algorithm for group decision making

Fuzzy relations are compared by membership values and as a consequence new types of local properties of fuzzy relations are introduced. In the new properties of fuzzy relations an arbitrary binary relation is involved. Particularly, a binary aggregation function may be used to define these properties. Connections between the new local properties of fuzzy relations are described. Furthermore, preservation of these properties in aggregation process is considered. Finally, notes on applications of the presented local properties in the context of fuzzy multisets and decision making are provided.